This research study investigates preventive maintenance management of diesel engine generators at the Nigerian Maritime Academy, Oron. An optimization methodology taking cognisance of equipment age was applied on failure data of diesel engine generators obtained from the institution’s maintenance data base to provide cost effective maintenance management / replacement programme for critical components of diesel engine generators. The analyzed results using Matlab provides a cost and reliability template which can be used to perform diesel generator maintenance management programme in the academy.

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Optimization of Preventive Maintenance Practice in Maritime
Academy Oron
Akpan, W. Aa
, Ogunsola T. Mb
a
Mechanical Engineering Department, University of Uyo
b
Boat and Shipbuilding Department, Maritime Academy, Oron
Abstract
This research study investigates preventive maintenance management of diesel engine generators at the Nigerian
Maritime Academy, Oron. An optimization methodology taking cognisance of equipment age was applied on
failure data of diesel engine generators obtained from the institution’s maintenance data base to provide cost
effective maintenance management / replacement programme for critical components of diesel engine
generators. The analyzed results using Matlab provides a cost and reliability template which can be used to
perform diesel generator maintenance management programme in the academy.
Keywords: Reliability, optimization, maintenance, modelling, maritime academy.
I. Introduction
The present Nigerian maritime academy Oron in Akwa Ibom State Nigeria started as a Nautical college of
Nigeria in 1979 with a mandate to train shipboard officers, ratings and shore-based management personnel and
in 1988 the college was upgraded to the present status and the mandate was expanded to training of all levels
and categories of personnel for all facets of the Nigerian maritime industry (Wikipedia, 2014).
The epileptic power supply in Nigeria has prompted the academy to generate its electricity for the
administrative activities of the institution using the diesel engine generators.
The diesel engine has become the overwhelming choice for marine industries both on board and off board.
This can be attributed to its, high performance. It has high reliability and a better fuel economy than
gasoline engine and is more efficient at light and full loads. The diesel engine generator emits fewer harmful
exhaust pollutants and is inherently safer because diesel fuel is less volatile than gasoline. However, diesel
engines can be ineffective under certain conditions, thus affecting engine performance especially when poor
diesel fuel quality is used and also when poor servicing and maintenance method is applied.
Maintenance is all actions which have the objective of returning a system back to another state. Thus,
maintenance has the ability to bring back the system quickly to its normal functional state and reduces
equipment down time (Moubray, 1995) and Tsang et al. (1999).
Maintenance can be categorized into two: corrective maintenance and preventive maintenance (Paz, 1994).
According to Koboa-Aduma (1991) Maintenance provides freedom from breakdown during operations.
Maintenance of equipment is essential in order to:
(i) keep the equipment at their maximum operating efficiencies;
(ii) keep equipment in a satisfactory condition for safe operations; and
(iii) reduce to a minimum, maintenance cost consistent with efficiency and safety.
Maintenance can be perfect and imperfect Pharm and Wang (1996) and Nakagawa (1987).
The Nigerian Maritime Academy Oron has among others 500KVA, 600KV and 800KVA diesel engine
generators to generate power for the administrative needs of the academy The maintenance costs of diesel
engine generators in the academy is on the increase. This is mostly caused by lack of clear maintenance
methodology by the institution to maintain these generators. The objective of this research is to conduct a
maintenance methodology on 500KVA, 600KVA and 800KVA diesel engine generators own by the academy
and to suggest ways maintenance and replacement actions should be performed on the generators with the
objective of reducing the cost of maintenance at the required reliability of the diesel engine generators.
II. Methodology
The data were collected from both primary and secondary sources. The primary data were obtained from the
log book for a period of three years. This data include the time of failure of the diesel engine generator, the
components causing the failure and also when the failed components were repaired or replaced. The secondary
information was obtained from maintainers, supervisors, engineers and managers. This information include:
maintenance cost, failure cost and replacement cost of each part. Ten critical parts in the diesel engine were
RESEARCH ARTICLE OPEN ACCESS

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selected for the study. The data formed input into a maintenance and replacement model by Kamran (2008).The
information was used to predict future maintenance planning for the three diesel generators in the next 60
months with the objective of reducing maintenance cost and increasing the reliability of the diesel generators
used by the institution.
III. Optimization model
The model by Kamran (2008) provides a general framework that was applied on the study. In the total cost
minimization equation, the constraints for the solution of the equation are as follows:
(i) Constraints that address the initial age of each component at the beginning of planning horizon.
Thus;
Xἰj = 0; 𝑖 = 1… N 1
where 𝑖 = component, j = period& N=No of components
(ii) Effective age of the components based on preventive maintenance activities recursively.
)()1)(1( '
1,11,1,1,,   jjjjijijiji iXmXrmX  2
𝑖 = 1… N and j = 2. . . T
J
T
XX jiji  ,
'
, 𝑖 = 1, N and j = 1. . . T 3
jiji rm ,,  ≤ 1; 𝑖 = 1. . . N and j = 1. . . T
Where: jiX , Effective age of component 𝑖 at the start of period j,
'
, jiX : Effective age of component 𝑖 at the end
of period j.
T = No. of periods, J = No. of intervals, jim , :
1
0
if component 𝑖 at period j is maintained, otherwise.
jir , :
1
0
if component 𝑖 at period j is replaced, otherwise, 𝛼𝑖: Improvement factor of component 𝑖
(iii) Condition/constraint preventing occurrence of simultaneous maintenance and replacement actions on the
components.
series
XXT
j
N
i RRe ijiijii



 )()((
1
,
'
,
4
jim , , jir , = 0 or 1; 𝑖 = 1. . . N and j = 1. . . T 5
jiX ,
'
, jiX ≥ 0 ; 𝑖 = 1, N and j = 1. . . T 6
Where𝜆𝑖: Characteristic life (scale) parameter of component 𝑖
𝛽𝑖: Shape parameter of component, 𝑖, RRseries: Required reliability of the series system of components.
Consider the case where component i is maintained in period j. For simplicity, it is assumed that the
maintenance activity occurs at the end of the period. The maintenance action effectively reduces the age of
component i at the beginning of the next period. That is:
Xi,j+1 =
'
, jiiX for i = 1,…, N; j=1,…,T and (0 ≤ α ≤ 1) 7
The term α is an “improvement factor”, similar to that proposed by Malik (1979), Jayabalan (1992). This factor
allows for a variable effect of maintenance on the aging of a system. When α = 0, the effect of maintenance is to
return the system to a state of “good-as new”. When α = 1, maintenance has no good effect, and the system
remains in a state of “bad-as-old”.
The maintenance action at the end of period j results in an instantaneous drop in the ROCOF of component i,.
Thus at the end of period j, the ROCOF for component i is )( '
ji Xv . At the start of period j + 1 ROCOF drops
to )0(iv
If component i is replaced at the end of period j, the following applies:
01, jiX =0 fori = 1,…,N; j=1,…,T 8

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i.e., the system is returned to a state of “good-as-new”. The ROCOF of component i instantaneously drops from
)( '
, jii Xv to )( '
, jii Xv
If no action is performed in period j, there is no effect on the ROCOF of component i and thus :
'
, jiX = jiX , +
𝑇
𝐽
for i = 1,…, N; j=1,…,T 9
'
1, jiX = jiX , for i = 1,…, N; j=1,…,T 10
iv (Xi,j+1) = )( , jii Xv for i = 1,…, N; j=1,…,T 11
T = No. of periods, j = No. of intervals, ROCOF = Rate of Occurrence of Failure
For a new system, the cost associated with all component levels of maintenance and replacement actions in
period j, remains as a function of all the actions taken during that period.
The expected number of failures of component i in period j, i
dttvNE i
jiX
Xji ji
)(][ .
,
'
,
 for i = 1,…, N; j= 1,…, T 12
Under the Non- homogenous piosson process assumption (NHPP) the expected number of component i failures
in period j is

 )()(][ ,
'
,, jiijiiji XXNE i
 for i = 1,…, N; j= 1,…, T 13
If the cost of each failure is iF , which in turn allows the computation of, F i j, the cost of failures attributable to
component i in period j is:
F i j = ][ , jii NEF for i = 1,…, N; j= 1,…, T 14
Hence regardless of any maintenance or replacement actions (which are assumed to occur at the end of the
period) in period j, there is still a cost associated with the possible failures that can occur during the period.
If maintenance is performed on component i in period j, a maintenance cost constant Mἰ is incurred at the
end of the period. Similarly If component i is replaced, in period j, the replacement cost is the initial purchase
price of the component i, be denoted by R i.
For a multi-component system, the cost structure is defined as stated above the problem can be reduced to a
simple problem of finding the optimal sequence of maintenance, replacement, or do-nothing for each
component, independent of all other components. That is, one could simply find the best sequence of actions for
component one regardless of the actions taken on component two and so on. This would result in N independent
optimization problems. Such a model seems unrealistic, as there should be some overall system cost penalty
when an action is taken on any component in the system. It would seem that there should be some logical
advantage to combine maintenance and replacement actions, e.g., while the system is shutdown to replace one
component, it may make sense to go ahead and perform maintenance/replacement of some other components,
even if it is not at its individual optimum point where maintenance or replacement would ordinarily be
performed. Under this scenario, the optimal time to perform maintenance/replacement actions on individual
components is dependent upon the decision made for other components. As such, a fixed cost of “downtime”, Z
, is charged in period j if any component (one or more) is maintained or replaced in that period. Consideration of
this fixed cost makes the problem much more interesting, and more difficult to solve, as the optimal sequence of
actions must be determined simultaneously for all components.
From the vantage point, at the start of period j = 0, it is right to determine the set of activities, i.e.,
maintenance, replacement, or do nothing, for each component in each period such that total cost is minimized.
In order to have X i j age of component i at the end of period j by using equation 2. First, define m i j, and r i j, as
binary variables of maintenance and replacement actions for component i in period j as:
jim ,
1
0
if component 𝑖 at period j is maintained, otherwise. 15
jir ,
1
0
if component 𝑖 at period j is replaced, otherwise. 16
The following recursive function of Xi j, X’ i j, m i j, r i j, α, with a constraint are constructed:
)()1)(1( 1,1,
'
1.1,1,,   jijijijijiji XmXrmX  17
J
T
XX jiji  '
,
'
, 18

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www.ijera.com 106 | P a g e
jim , + jir , ≤1 19
In addition, the initial age for each component is equal to zero:
jiX , =0 for i =1,…,N 20
If component replacement occurs in the previous period then,
1, jir = 1, jim =0, 21
jiX , . If a component is maintained in the previous period then
1, jir = 1, jim =1 22
jiX , =
'
1, jiiX 23
and finally if nothing is done,
1, jir =o, 1. jim = 0 and jiX , =
'
1, jiX 24
which corresponds to our basic assumptions given in equation one. From the definitions of each type of cost, the
total cost function is:
))]1(1([)))()([( .,
1 1
,,,,,
'
,
1 1
min jiji
T
j
N
i
jijijijijiJIi
N
i
N
j
iimum rmZrRmMXXFCostTotal ii
     


Subject to: 25
0, jiX . i=1….N 26
)()1)(1( 1,1,
'
1.1,1,,   jijijijijiji XmXrmX  i=1…N, j=2…T 27
J
T
XX jiji  '
,
'
, i=1….N, j=1….T 28
jim , + jir , ≤1 i=1….N, J=1….T 29
series
XXT
j
N
i RRe ijiijii



 )()((
1
,
'
,
jim , , jir , = 0 or 1; 𝑖 = 1. . . N and j = 1. . . T 30
jiX ,
'
, jiX ≥ 0 𝑖 = 1, N and j = 1. . . T 31
This objective function computes the total minimum cost subject to the above stated constraints with input
parameters from tables 1, 2 and 3.
The generalized reduced gradient and the simulated annealing algorithms were used to solve the cost
minimization using Matlab software and the results presented in tables 4, 5 and 6. Tables 1, 2 and 3 were
generated based on data obtained from maintenance log book and information from maintenance engineers.
IV. Results and discussion
The characteristic life  , shape factor  , maintenance factor , failure cost, maintenance cost, and
replacement cost are presented in tables 1, 2 and 3 for 500KVA, 600KVA and 800KVA diesel generators
respectively for the selected components shown in tables 1.2 and 3.
Table 1 Parameters for 500KV a diesel generator
Mo
nth
Component λ(Days) β ∝
Failure
Cost (N)
Maintenanc
e Cost (N)
Replacement
Cost (N)
1. Injector Pump 950 0.0005 0.00025 128,000.00 68,000.00 91,000.00
2. Calibration of Valve 1080 0.0007 0.00025 340,000.00 32,000.00 180,000.00
3. Cutting of Ring 1090 0.0004 0.00025 210,000.00 80,000.00 170,000.00
4. Top Gasket Cylinder
Replacement
1170 0.0004 0.00025 260,000.00 80,000.00 183,000.00
5. Radiator 1050 0.0004 0.00025 96,000.00 16,000.00 36,000.00
6. Oil Pump 1005 0.0004 0.00025 80,000.00 16,000.00 80,000.00

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7. Injector Nuzzle 900 0.0005 0.00025 270,000.00 80,000.00 270,000.00
8 Air Filter 1160 0.0004 0.00025 120,000.00 40,000.00 80,000.00
9 Alternator 250 0.0006 0.00025 154,000.00 46,000.00 85,000.00
10 Water Pump 1050 0.0005 0.00025 87,000.00 40,000.00 70,000.00
The characteristics life and shape factors were calculated from failure data while the failure costs,
maintenance costs and replacement costs data were obtained from maintenance engineers. The maintenance
factors were assumed based on the frequency of failure of components.
Table 2 Parameters for 600KV a diesel generator
Month
Component λ(Days) β ∝
Failure
Cost (N)
Maintenanc
e
Cost (N)
Replacement
Cost (N)
1. Injector Pump 1100 0.0007 0.00010 128,000.00 68,000.00 91,000.00
2. Calibration of Valve 800 0.0006 0.00010 340,000.00 32,000.00 180,000.00
3. Cutting of Ring 470 0.0003 0.00010 240,000.00 80,000.00 190,000.00
4. Top Gasket Cylinder
Replacement
1020 0.0005 0.00010 310,000.00 80,000.00 189,000.00
5. Radiator 1020 0.0004 0.00010 96,000.00 16,000.00 36,000.00
6. Oil Pump 800 0.0005 0.00050 80,000.00 16,000.00 80,000.00
7. Injector Nuzzle 900 0.0005 0.00050 270,000.00 80,000.00 270,000.00
8 Air Filter 1200 0.0006 0.00050 160,000.00 40,000.00 110,000.00
9 Alternator 990 0.0006 0.00050 210,000.00 76,000.00 115,000.00
10 Water Pump 780 0.0007 0.00050 87,000.00 40,000.00 70,000.00
The failure cost is higher than replacement cost which in the same vain higher than the maintenance cost. The
costs of components in 600KVA, 700KVA and 800KV generators are different in some cases or similar in
others.
Table 3 Parameters for 800KV a diesel generator engine
Month
Component λ(Days) Β ∝
Failure
Cost (N)
Maintenance
Cost (N)
Replacement
Cost (N)
1. Injector Pump 900 0.0005 0.00022 128,000.00 68,000.00 91,000.00
2. Calibration of Valve 1050 0.0004 0.00035 340,000.00 32,000.00 180,000.00
3. Cutting of Ring 1050 0.0005 0.00038 210,000.00 80,000.00 170,000.00
4. Top Gasket Cylinder
Replacement
980 0.0007 0.00034 33,600.00 6,720.00 28,800.00
5. Radiator 1010 0.0003 0.00032 310,000.00 80,000.00 189,000.00
6. Oil Pump 1015 0.0003 0.00028 96,000.00 16,000.00 36,000.00
7. Injector Nuzzle 1020 0.0003 0.00015 80,000.00 16,000.00 80,000.00
8 Air Filter 1030 0.0005 0.00012 270,000.00 80,000.00 170,000.00
9. Alternator 1010 0.0003 0.00025 270,000.00 80,000.00 170,000.00
10. Water Pump 1110 0.0006 0.00020 120,000.00 40,000.00 80,000.00
In tables 4, 5 and 6 the minimum required reliability is presented in the third column by the decision maker,
while a search algorithm of generalized reduced gradient and simulated annealing calculate the total optimized
cost function for each component and the optimum reliability in the sixth column using Matlab software. A gap
analysis shows the effectiveness of each algorithm. At 98% reliability and a total optimized cost of 7,082,250.51
naira, six number periods at ten months per period for the 60 months prediction has the highest cost. This is
expected because of the high expected reliability of 98% and long period of maintenance. However this option
is less preferable to 36 number of periods and about 1.7 months per period and a cost of 960,421,43 naira by
generalized gradient method at a reliability of 50% for the 500KVA diesel generator as shown in table 4.

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Table 4 Required reliability and total cost optimized function for 500KV diesel generator
However for the 600KVA and 800KVA diesel engine generators, 48 periods , representing an interval of
1.25 months, has the lowest cost of 950,421,43 naira at 50% reliability. This formulation presents different
options for the decision maker and is effective in making maintenance management decisions for the assets.
Table 5 Required reliability and total cost optimized function for 600KVA diesel generator
No. of
components
Number of
periods
Required
Reliability
Algorithm
Total cost optimized
function value (OFV)
Reliability
(%)
OFV Gap
10 6 97 Generalized reduced
Gradient (GRG)
2,965,264.07 70.00 -
Simulated
Annealing (SA)
3,154,952.01 69.64 6.40%
12 90 GRG 5,693,688.96 90.00 -
SA 6,049,626.347 90.02 6.25%
18 80 GRG 2,675,884.570 80.00 -
SA 2,839,417,283 79.80 6.11%
24 70 GRG 1,143.506.918 70.00 -
SA 1,216,657.052 69.64 6.40%
30 60 GRG 3.576,008.178 60.00 -
SA 3,812,394.917 59.93 6.61%
36 50 GRG 2,264,196.091 50.00 -
SA 2,416,235.994 49.00 6.71%
42 97 GRG 3,732,178.10 60.00 -
SA 3,913,284.73 60.54 4.85%
48 90 GRG 960,421,43 50.00 -
SA 1,006,157.79 49.47 4.76%
54 80 GRG 1,467,308.49 97.00 -
SA 1,549,307.76 97.02 5.59%
60 70 GRG 2,127,321.16 90.00 -
SA 2,260,309.31 90.02 6.25%
No. of
components
Number of
periods
Required
Reliability
Algorithm
Total cost optimized
function value (OFV)
Reliability
(%)
OFV Gap
10
6 98
Generalized reduced
Gradient (GRG)
7,082,250.51 98.00 -
Simulated Annealing
(SA)
7,499,248.68 97.95 5.89%
12 90 GRG 1,840,017.981 97.00 -
SA 1,942,845.804 97.02 5.59%
18 80 GRG 4,767,597.09 90.00 -
SA 5,014,618.05 90.01 5.17%
24 70 GRG 2,813,854.26 70.00 -
SA 2,950,837.53 69.50 4.87%
30 60 GRG 3,732,178.10 60.00 -
SA 3,913,284.73 60.54 4.85%
36 50 GRG 960,421,43 50.00 -
SA 1,006,157.79 49.47 4.76%
42 97 GRG 1,467,308.49 97.00 -
SA 1,549,307.76 97.02 5.59%
48 90 GRG 2,127,321.16 90.00 -
SA 2,260,309.31 90.02 6.25%
54 80 GRG 1,156,146.96 80.00 -
SA 1,226,803.17 79.80 6.11%
60 70 GRG 2,965,264.07 70.00 -
SA 3,154,952.01 69.64 6.40%

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ISSN : 2248-9622, Vol. 5, Issue 5, ( Part -6) May 2015, pp.103-109
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Table 6 Required reliability and total cost optimized function for 800KVA diesel generator
No. of
components
Number of
periods
Required
Reliability
Algorithm
Total cost optimized
function value (OFV)
Reliability
(%)
OFV Gap
10 6 80 Generalized reduced
Gradient (GRG)
1,885,488.0 80.00 -
Simulated
Annealing (SA)
2,000,716.8 79.80 6.11%
12 70 GRG 1,968,848.0 70.00 -
SA 2,094,795.2 69.64 6.40%
18 60 GRG 2,061,760.0 60.00 -
SA 2,198,049.6 59.93 6.61%
24 97 GRG 1,182,446.4 97.00 -
SA 1,248,526.4 97.02 5.59%
30 90 GRG 1,586,476.8 90.00 -
SA 1,685,654.4 90.02 6.25%
36 50 GRG 2,207,536.0 50.00 -
SA 2,355,771.2 49.00 6.71%
42 97 GRG 3,732,178.10 60.00 -
SA 3,913,284.73 60.54 4.85%
48 90 GRG 960,421,43 50.00 -
SA 1,006,157.79 49.47 4.76%
54 80 GRG 4,767,597.09 90.00 -
SA 5,014,618.05 90.01 5.17%
60 70 GRG 2,786,005.66 80.00 -
SA 2,918,223.78 80.00 4.75%
V. Conclusions
The results presented from the research show that Kamran (2008) formulation can be used in maintenance
decision making for diesel engine generators. The research also shows that shorter maintenance interval is much
preferable for multiple component equipment at an optimum reliability of 50%. From the results, the generalized
gradient method algorithm provides a lower total optimized cost compared to simulated annealing method and
therefore recommended in solving such problems. This methodology is therefore recommended to the Maritime
Academy Oron for effective maintenance management programme for the diesel engine generators.
References
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Ph.D thesis, University of Louisville, Kentucky, USA.
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Nigeria, Nsukka. 243
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[10] Wikipedia (2014) Maritime Academy of Nigeria : Available [Online] http//en.wikipedia.org